In light of recent interest in adjoint modelling in underwater acoustics, we present a selective review which is mainly focused on the underlying concept of backpropagation. The different implementations of that concept to date are compared and discussed in the framework of experimental acoustic inversion in shallow water with application to source localisation, ocean acoustic tomography, geoacoustic inversion and underwater communications. Well established inversions or focalisation methods based on matched field processing, model-based matched filter and time reversal mirror are related to less popular ones such as acoustic retrogation and other variants of backpropagation. In contrast to the latter, adjoint-based, variational inversion approaches make use of the adjoint of a forward model to backpropagate the model-data mismatch at the receiver toward the source. The paper describes in greater detail adjoint methods and applications in underwater acoustics. We also present results using environmental data obtained during a geoacoustic inversion experiment in the Mediterranean.